QJEEM17Ph0e34: JEE Main 2017 Physics - Class 11 JEEM17Ph0e34 Solution: A man grows into a giant such that his linear dimensions…

To determine how the stress in the leg changes when a man's linear dimensions increase by a factor of 9, we can analyze the relationship between the dimensions and the stress on the legs.

First, let's establish some relationships:

1. Linear dimensions (length, width, height) increase by a factor of 9.


2. Density remains the same.

Stress is defined as force per unit area:

$$\text{Stress}={\displaystyle \frac{\text{Force}}{\text{Area}}}$$

Since density remains constant, the volume and thus the mass of the man will change according to the cube of the linear dimensions. Since the linear dimension changes by a factor of 9, the volume (and hence the mass) changes by a factor of:

$$9^3=729$$

Therefore, the weight (force due to gravity) also increases by a factor of 729.

The cross-sectional area of the leg is proportional to the square of the linear dimensions. Thus, if the linear dimension increases by a factor of 9, the cross-sectional area increases by a factor of:

$$9^2=81$$

Now, substituting these factors into the stress formula:

$$\text{New Stress}={\displaystyle \frac{\text{New Force}}{\text{New Area}}}={\displaystyle \frac{729\times \text{Original Force}}{81\times \text{Original Area}}}$$

Simplifying, we get:

$$\text{New Stress}=9\times {\displaystyle \frac{\text{Original Force}}{\text{Original Area}}}=9\times \text{Original Stress}$$

Thus, the stress in the leg increases by a factor of 9. Therefore, the correct answer is:

Option B: 9